KR101436077B1 - Light emitting element and method for manufacturing same - Google Patents

Abstract

(Structural body) having different refractive indexes, wherein the interface of the two systems (structures) satisfies the conditions of Bragg scattering and the photonic crystal periodic structure having a photonic band gap is provided in the light- The semiconductor light emitting device comprising:

Description

TECHNICAL FIELD [0001] The present invention relates to a light emitting device,

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a light emitting device and a method of manufacturing the same.

Among light emitting devices, LED (Light Emitting Diode) devices are being put to practical use as light emitting devices of high luminance and energy saving type.

For example, an LED, which is a semiconductor light emitting element using a nitride semiconductor (to be referred to as " GaN " hereinafter), is expected as a light source for an illumination that changes into a fluorescent lamp. Performance is improved by improving lumens / In terms of cost, development is being actively pursued with the aim of lowering price / lumen. In the active layer, the light emitted from the recombination of holes and electrons is emitted from the GaN to the air. Since the refractive index of GaN is about 2.5 higher than the refractive index of air, about 70% of the light at the interface with the air is totally reflected And finally it is turned into heat and disappears. Therefore, how to take out the light in the GaN in the future is a big problem in performance improvement and cost reduction.

High-brightness LEDs emit deep ultraviolet rays with a wavelength of 220 to 350 nm. They are used in sterilization, water purification, medical fields, high-density optical recording, high-color-rendering LED lighting, Applications in a wide range of fields such as high-speed decomposition treatment of pollutants are expected. However, until now, the external quantum efficiency of the external LED is about several percent, which is considerably smaller than the value of several tens of percent of the blue LED, making it difficult to put it into practical use.

The external quantum efficiency (EQE) of the LED is determined by multiplying the internal quantum efficiency (IQE), the electron injection efficiency (EIE) and the light extraction efficiency (LEE) (EQE = IQE x EIE x LEE), the improvement of the light extraction efficiency contributes to the improvement of the efficiency together with the internal quantum efficiency and the electron injection efficiency.

1A, for example, an n-type AlGaN layer 5 / an AlN buffer layer 3 and an active layer made of an AlGaN / GaN multiple quantum well (hereinafter referred to as an AlGaN active layer) are formed on a sapphire substrate 1 A p-type AlGaN layer 9, and an Ni / Au electrode layer 11, as shown in Fig. In the n-type AlGaN layer 5, an n-type electrode 4 is formed.

The light emitted by the recombination of holes and electrons in the AlGaN active layer 7 is transmitted through the sapphire substrate 1 as shown by arrows L1 to L3 and radiated into the air from the back surface 1a thereof (light extraction surface). Here, the refractive index of sapphire with respect to the index of refraction of air is as high as approximately 1.82, so that the critical angle? C at the interface between the back surface 1a of the sapphire substrate and the air from the Snell's law (sin? I = 1 / The incident light exceeding the critical angle? C is trapped in the nitride semiconductor layers 3, 5, and 7 or the sapphire substrate 1 by total internal reflection, (L2, L3). Since the ratio of light lost by this heat reaches 70 to 90%, how to extract the light that is lost inside is an issue of performance improvement.

The blue LED shown in Fig. 1B has an n-type electrode 24, an n-type GaN layer 23, an active layer 25 made of GaN or the like, a p-type GaN layer 27, , An ITO transparent electrode layer 29, SiO ₂ A protective film 31 is formed. The light emitted from the GaN active layer 25 is incident on the substrate side and the SiO ₂ The light is emitted in the vertical direction on the side of the protective film, and more than 50% of the light emitted to the air from the upper protective film (for example, refractive index of 1.46 in the case of SiO ₂ ) exceeds the critical angle and is totally deflected. Thus, at the interface between the lower n-type GaN layer 23 (refractive index is 2.50) and the sapphire substrate 21 (wavelength 455 nm, refractive index is 1.78), the light emitted from the n-type GaN layer 23 to the sapphire substrate 21 There is a problem that light of less than 50% is totally reflected in the same way and disappears inside.

In order to solve such a problem, for example, in Patent Document 1 below, a photonic crystal periodic structure having a photonic band gap is used as a photonic crystal periodic structure in which a p-type nitride semiconductor layer, Holes open in the stacking direction are formed so as to block light traveling through a waveguide parallel to the semiconductor layer and to take out light from above and below in the stacking direction of the semiconductor layers.

In Patent Document 2, the photonic crystal periodic structure in which the period is set to a value which is 1/4 to 4 times the wavelength of light emitted from the active layer is provided on the back surface of the sapphire substrate, thereby suppressing total reflection from the back surface of the sapphire substrate, It is devising to extract light.

Patent Document 3 discloses that a photonic crystal periodic structure having a photonic band is provided as a pore in the active layer so as to cut off light traveling through a waveguide parallel to the active layer and the upper and lower semiconductor layers, .

Further, in Patent Document 4, a photonic crystal periodic structure having a photonic band is provided in an n-type semiconductor layer from which a sapphire substrate is removed after preparing a predetermined LED structure, and the light is taken out from the n-type semiconductor layer .

In Patent Document 5, a convex portion periodic structure (moth-eye structure) of 1/3 or less of the emission wavelength is provided at the interface between the sapphire substrate and the nitride semiconductor layer, and the total reflection at this interface is suppressed And light was taken out from the back surface of the substrate.

Patent Document 6 discloses a photonic crystal periodic structure having a photonic band gap, in which a hole passing through an ITO transparent electrode, a p-type semiconductor layer, an active layer, and an n-type semiconductor layer is provided, So that light is taken out in the vertical direction perpendicular to these layers.

In the following non-patent document 1, a periodic structure having a morphology is provided on the back surface of a sapphire substrate to suppress total reflection from the back surface of the sapphire substrate, thereby making it possible to extract light.

Patent Document 1: Japanese Patent No. 4610863 Patent Document 2: Japanese Patent No. 4329374 Patent Document 3: Japanese Patent Application Laid-Open No. 2008-311317 Patent Document 4: Japanese Patent Specification No. 2006-523953 Patent Document 5: JP-A-2010-74090 Patent Document 6: Japanese Patent Application Laid-Open No. 2011-86853

Non-Patent Document 1: Development of DUVLED at the Japan Cement Association "Wide Gap Semiconductor Optoelectronic Devices 162th Committee" 74th Research Meeting Source: Changkwang Science (UV Craftory Co., Ltd)

However, in the photonic crystal periodic structure or the morphotropic periodic structure in Patent Documents 1 to 6 and Non-Patent Document 1, specific laws and methods for finding optimum parameters in the periodic structure for maximizing the light extraction efficiency It is not described at all.

In Patent Documents 1, 3, and 6, each of the documents is disclosed in which the vacancies are formed vertically through the n-type nitride semiconductor layer, the nitride semiconductor active layer, the p-type nitride semiconductor layer, Periodic structure. The resistance of the nitride semiconductor increases as the size of the openings in the nitride semiconductor increases, resulting in a decrease in the internal quantum efficiency. As a result, the external quantum efficiency decreases and the luminance decreases. In addition, the total light extraction efficiency is not maximized within a periodic structure having a photonic band gap, and there is no disclosure of specific structural parameters of the periodic structure.

In Patent Document 2, since the periodic structure is provided on the back surface of the sapphire substrate, a decrease in the internal quantum efficiency is small. However, since the periodic structure having no photonic band gap is used, Which is lower than that of the device of FIG.

When the structure of Patent Document 5 is applied to an extra-luminescent LED and a nitride semiconductor layer is crystal-grown on the convex structure on the surface of sapphire, abnormal nucleation occurs and the internal quantum efficiency is lowered. Further, the light emitted from the active layer travels toward the convex periodic structure on the sapphire surface, which is different from the structure in which the transmittance of light is increased by suppressing total reflection because it is a moth eye structure that suppresses Fresnel reflection. Further, there is no advantage in that the front luminance due to the refracting effect of complex light seen when the photonic crystal having the photonic band gap is used.

In the non-patent reference 1, since the periodic structure is provided on the back surface of the sapphire substrate, it is possible to suppress the decrease in the internal quantum efficiency. However, the periodic structure is a MOS-IH structure, But to suppress Fresnel reflection. Also, the front luminance can not be increased.

In Patent Document 4, a photonic crystal periodic structure having a photonic band gap is provided on the back side of the n-type nitride semiconductor layer. The back surface of this layer has a composition richer in N (nitrogen) than Ga, and since it is unstructured as a structure, it is difficult to planarize this surface, and it is difficult to provide a photonic crystal periodic structure requiring high precision, . In addition, the light extraction efficiency is not maximized only within the periodic structure having the photonic band gap. In addition, a nanoimprint apparatus is used for the lithography of this periodic structure, but when the resin mold is not used, it is difficult to transfer the substrate along with warpage or minute protrusions. When a nitride semiconductor layer is crystal-grown on a sapphire substrate, crystal growth is performed at a high temperature close to 1000 ° C. due to a difference in thermal expansion coefficient between the sapphire substrate and the nitride semiconductor, and then the substrate is returned to room temperature. Even if the sapphire substrate is peeled after the supporting substrate is bonded to the p-type nitride semiconductor layer after the crystal growth with the n-type nitride semiconductor layer, the active layer, and the p-type nitride semiconductor layer, Or minute concavities and convexities are not solved, the process becomes complicated such as microfabrication after the planarization process.

Normally, a technique called photolithography is used for micromachining of a nm order. As a typical apparatus, a stepper, an aligner, an electron beam drawing apparatus, or the like can be given. The stepper or aligner can accommodate a large area of 6 to 10 inches, but can not accommodate warping of about 100 microns of a large substrate. The throughput of the electron beam drawing apparatus is not suitable for mass production.

In addition, even when the organic resist is transferred into a desired periodic structure by dry etching after transferring the nanoimprint lithography, the shape after the etching does not become the periodic structure as designed.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a high-brightness semiconductor light emitting device having enhanced light extraction efficiency as a result of which the front brightness is emphasized in view of the problems of the related art as described above. It is another object of the present invention to provide a method of designing a photonic crystal periodic structure having a photonic band gap enabling high brightness. It is also an object of the present invention to provide a manufacturing method for processing a periodic structure according to a design in a desired region.

An object of the present invention is to provide a device in which a photonic crystal structure is provided in an LED element in particular to improve both external quantum efficiency and luminance directivity by improvement of light extraction efficiency and a manufacturing method thereof.

The present invention is characterized in that a concavo-convex portion made of a two-dimensional photonic crystal having a period equal to the wavelength of the light medium is processed on the back surface of the sapphire substrate or on the interface between the surface of the sapphire substrate and the GaN layer, (Photonic band gap) in which transmission of light becomes impossible.

Light having a wavelength within the photonic bandgap is not transmitted through the plane in which the periodic structure is formed but is transmitted only in a direction perpendicular to this plane. Therefore, the light emitted from the active layer and reaching the interface of the sapphire substrate or the sapphire substrate surface and the GaN layer, or the protective film, is not totally reflected at the interface with the air and is released into the air.

The present invention is characterized in that a photonic crystal periodic structure satisfying a condition that an interface of two structures having different refractive indexes satisfies Bragg scattering conditions and has a photonic band gap is provided in the light-extraction layer Semiconductor light emitting element.

Particularly, by selecting a photonic crystal periodic structure in which the photonic band gap is maximized, the light extraction efficiency is improved, and as a result, the frontal brightness can be emphasized.

In the substrate, such as in the structure of the semiconductor light emitting element, the light-emitting layer is not a sapphire crystal layer, a GaN-based, SiO ₂ It is preferable that the protective film is formed at any one of the protective films.

The present invention also provides a semiconductor light emitting device having a photonic crystal periodic structure in which a light emitting surface is provided on a back surface of a substrate, an AlN buffer layer provided on the substrate, an n-type AlGaN layer provided thereon, And a p-type AlGaN layer provided thereon, wherein the light-extracting surface satisfies the conditions of Bragg scattering and has a photonic band gap, and is preferably a maximum.

Or the semiconductor light emitting device having the photonic crystal periodic structure has a light extraction surface on a substrate surface, an n-type GaN layer provided on the substrate, an active layer provided thereon, a p-type GaN layer provided thereon, A transparent electrode layer provided on the transparent electrode layer, and a protective film as a light-extracting surface provided thereon, wherein the light-extracting surface satisfies the conditions of Bragg scattering and has a photonic band gap, and is preferably a maximum.

In the above configuration, the reason why the photonic band gap becomes maximum is for the following reason.

The plane wave output from the photonic crystal periodic structure satisfies the condition of Bragg scattering (m? / N _av = 2a, m: order,?: Wavelength of light in vacuum, n _av : average refractive index, ) And a magnetic field H developed by Maxwell's electromagnetic wave equation

^{Σε -1 (GG ') | k} + G || k + G' | E (G ') = ω 2 / c 2 E (G')

And

^{Σε -1 (GG ') (k} + G) * (k + G') H (G ') = ω 2 / c 2 H (G)

.

(Ε ^-1 : reciprocal of dielectric constant, G: reciprocal lattice vector, ω: frequency, c: flux, k: wavenumber vector).

Solving the eigenvalue problem of the above equation, a band structure representing the dispersion relationship between the frequency (?) And the wave number vector k is obtained as TE (Transversal Electric) light and TM (Transversal Magnetic) light, respectively. These TE, TM light each minimum value of the dielectric band maximum value ω ₁ a / 2πc the air band (second photonic band of the first photonic band) ω ₂ a / difference 2πc, i.e., photonic band gap = ω ₂ (period (a), diameter (d)) satisfying the relation that the value of a / ₂ ? c-? ₁ a / ₂ ? c becomes the maximum is obtained and the periodic structure is designed on the basis thereof. This numerical value is analyzed by the FDTD method (time domain differential method) to confirm that the optimum value of the depth h of the periodic structure, the luminance improvement ratio, and the good and bad light distribution are confirmed.

Next, a master mold for nanoimprinting is formed. A resin mold is prepared to cope with the warpage of the substrate, and is transferred to the resist on the substrate using the resin mold. The pattern on the substrate and the master mold pattern are not reversed. After the nanoimprint, the substrate is etched by ICP dry etching. At this time, the selection ratio of the etching gas and the resist is largely changed depending on the material of the part to be processed, so that it is difficult to control the shape and size of the irregularities initially intended.

Therefore, it is necessary to grasp the material of the portion to be processed and the etching bias of the resist in advance or to select an appropriate resist. Here, a mold is formed at a period (a), a diameter (d), and a depth (h) obtained by the above design method, a resin mold is taken therefrom, a pattern is transferred to a resist on the substrate with a nanoimprint, Remove the resist and measure the actual shape. The difference between this measured value and the design value is the etching bias value. The master mold is again formed by reflecting the etching bias value, and the photonic crystal periodic structure as designed is completed on the back surface of the sapphire substrate or on the interface between the sapphire substrate surface and the GaN layer or on the protective film (Referred to as process integration). The present invention forms a band structure with respect to light on the interface by processing a concavo-convex portion made of a two-dimensional photonic crystal having a period equal to the wavelength of the light medium in the interface or the interface between the sapphire substrate surface and the GaN layer, There is an energy region (photonic band gap) in which transmission becomes impossible. Light having a wavelength within the photonic bandgap is not transmitted through the plane in which the periodic structure is formed but is transmitted only in a direction perpendicular to this plane. Therefore, the light emitted from the active layer and transmitted through the sapphire substrate, or the interface between the sapphire substrate surface and the GaN layer, or the protective film, is not totally reflected at the interface with the air and is released into the air. As a result, the light extraction efficiency is improved, The luminance increases. In addition, the light emitting device has a high frontal luminance.

More specifically, the present invention relates to a light emitting device comprising: a first conductive type GaN layer; an active layer; a second conductive type GaN layer; and a second conductive type GaN layer or a second conductive type GaN layer, (Structure) having a substrate or a protective film for forming an extraction layer and having a periodic structure composed of two systems (structures) having different refractive indices, the interface of the two systems (structure) satisfying Bragg scattering conditions and having a photonic band gap And has a photonic crystal periodic structure in a light-extraction layer.

The two systems (structures) having different refractive indexes include, for example, air and sapphire substrates, sapphire substrates and GaN layers, air and SiO ₂ And a protective film.

It is preferable that the light extracting layer is a substrate of the semiconductor light emitting element or a protective film formed on the side opposite to the substrate.

The photonic crystal periodic structure may be provided in an area at an arbitrary depth position of the substrate.

The photonic crystal periodic structure may be formed so as to include holes formed periodically on the back surface of the substrate. In addition, the public includes those with the bottom.

The photonic crystal periodic structure may be formed at two or more positions within a region at an arbitrary depth position in one light extraction layer or at least two or more photodetection layers may be formed at any depth position of each of the substrate and the protection film At least two locations in total may be formed.

Examples of the formation of the one light-extraction layer include a semiconductor light-emitting element in which the photonic crystal periodic structure is formed on both the front and back surfaces of a sapphire substrate in a face down (flip chip) structure.

As an example of forming the two or more light-extraction layers, there is a semiconductor light-emitting element in which the photonic crystal periodic structure is formed on both the surface of a sapphire substrate as a light extraction layer and the surface of a protective film such as SiO ₂ in a face-

The photonic crystal periodic structure having the photonic band gap has a structure in which a plane wave output from the photonic crystal periodic structure is divided into an electric field E and a magnetic field H,

^{Σε -1 (GG ') | k} + G || k + G' | E (G ') = ω 2 / c 2 E (G') and ^{Σε -1 (GG ') (k} + G) * (k + G') H (G ' ) = ω ² / c ² H (G), (ε ^-1 : reciprocal of permittivity, G: reciprocal lattice vector, ω: frequency, c: flux, k:

(A) and the diameter (d) of the structure are determined by the difference between the dielectric band (first photonic band) and the air band (second photonic band) among the TE light or TM light obtained from the eigenvalue calculation ) Is determined on the basis of the photonic crystal periodic structure. And the depth (h) is determined by the FDTD method.

The method of determining the depth h by the FDTD method is to maximize the LEE increase rate based on the increase rate of the sidewall LEE of the light emitting element, the increase rate of the light extraction surface LEE, and the increase rate of the LEE at both the sidewall and the light extraction surface (A), and the value thereof is 0.5 times or more the period (a).

Characterized in that the photonic crystal periodic structure of the light extraction layer is processed by a nanoimprint lithography method. And is processed using transfer through a resin mold. The substrate may be sapphire.

The semiconductor layer of the semiconductor light emitting device is preferably made of a nitride semiconductor.

And the following processes 1) to 3) are used in the nanoimprint lithography method.

1) When a master mold for a nanoimprint is prepared, a resin mold is prepared to cope with the warping of the substrate, and transferred to the resist on the substrate by using the resin mold so that the pattern on the substrate and the master mold pattern are not reversed do.

2) The substrate is etched by dry etching after nanoimprinting. At this time, a mold is formed at a period (a), a diameter (d) and a depth (h), a resin mold is taken therefrom, a pattern is transferred to a resist on the substrate by a nanoimprint, the resist is removed by dry etching, .

3) The difference between the measured value and the design value is the etching bias value, and the master mold is again formed by reflecting the etching bias value, and the transfer, dry etching, and resist residues are removed.

The present invention relates to a semiconductor light emitting device having a periodic structure provided in a semiconductor light emitting device and composed of two systems (structures) having different refractive indices, wherein the interface between the two systems (structure) satisfies Bragg scattering conditions and has a photonic band gap 1. A structural parameter calculation method for obtaining parameters of a photonic crystal periodic structure, the method comprising the steps of: measuring a plane wave output from the photonic crystal periodic structure by an electric field (E) and a magnetic field (H)

^{Σε -1 (GG ') | k} + G || k + G' | E (G ') = ω 2 / c 2 E (G') and ^{Σε -1 (GG ') (k} + G) * (k + G') H (G ' ) = ω ² / c ² H (G), (ε ^-1 : reciprocal of permittivity, G: reciprocal lattice vector, ω: frequency, c: flux, k:

(First photonic band) from the calculation of the eigenvalues of the air bands (second photonic band) and the TE band (first photonic band) And a second step of determining a period (a) and a diameter (d) which are parameters of the periodic structure.

(A) to (m) by inputting a wavelength (λ), a degree (m), and an average refractive index (n _av ) to the Bragg scattering condition in the first step, (Ε ₁ , ε ₂ ) of the radius r of the first system and the radius R of the circular hole constituting the period from the determined period a are determined for each order m, (? ₁ ,? ₂ ) and R / a, which are obtained by multiplying the refractive index (n ₁ , n ₂ ) by the refractive index (n ₁ , n ₂ ) and inputting the obtained wavelength λ, permittivity (ε ₁ , ε ₂ ) and R / a into the Maxwell electromagnetic wave equation.

In step S1, R / a (0.15 < R / a < 0.45) is determined from the circular hole R and the period a constituting the photonic crystal. Further, the refractive index (n ₁ , n ₂ ) of the medium constituting the above and the average refractive index (n _av ) from R / a are obtained.

It is also preferable to have a third step of determining the depth (h) by the FDTD method.

Also, the depth h determined in the third step is preferably determined by parameter calculation using a value at least 0.5 times the period (a).

According to the present invention, the light extraction efficiency in the semiconductor light emitting device is also improved, thereby increasing external quantum efficiency and brightness. In addition, the front luminance can be improved.

This specification includes contents described in the specification and / or drawings of Japanese Patent Application No. 2011-154276, which is the basis of the priority of the present application.

1A is a diagram showing an example of the configuration of an extra-bright LED.
Fig. 1B is a diagram showing a configuration example of a blue LED.
2A is a diagram showing a first example of a configuration of a high-brightness semiconductor-based external LED according to an embodiment of the present invention.
Fig. 2B is a diagram showing a second configuration example of a high-brightness semiconductor-based external LED according to the embodiment of the present invention.
2C is a diagram showing a third example of the structure of a high-brightness semiconductor-based external LED according to the embodiment of the present invention.
2D is a diagram showing a first configuration example of a high-luminance semiconductor blue LED according to an embodiment of the present invention.
2E is a diagram showing a second configuration example of a high-luminance semiconductor blue LED according to the embodiment of the present invention.
2F is a diagram showing a third example of the structure of a high-luminance semiconductor blue LED according to the embodiment of the present invention.
Fig. 3 is a view corresponding to Fig. 2A (b), and shows the shapes of the hole 15a and the remaining portion 15b viewed from the rear surface of the substrate.
Fig. 4 is a flowchart showing an example of processing when the depth h of step S7 is a variable of the diameter d (2R) (0 < h < 1.0d).
5 is a flowchart showing an example of processing when the depth h of step S7 is a variable of period a (0 <h <1.0a).
Fig. 6 is a diagram showing an example of a procedure for obtaining an average refractive index (n _av ).
7 is a diagram showing an example of the calculation result of the band structure at R / a = 0.4.
8 is a diagram showing a grating band structure in a case where the sapphire surface is flat as a comparison object.
9 is a diagram (R / a = 0.25) obtained by interpreting across the first Brillouin zone and obtaining the isocentric frequency plane for the wavenumber vector (kx, ky) of the? 2 TE band.
10 is a diagram (R / a = 0.4) obtained by interpreting across the first Brillouin region and obtaining the iso-frequency surface with respect to the wavenumber vector (kx, ky) of the? 2 TE band.
11 is a diagram showing the relationship of the refraction angle with respect to the incident angle when R / a = 0.25.
12 is a diagram showing the relationship of the refraction angle with respect to the incident angle when R / a = 0.4.
13 is a diagram showing an example of a FDTD method simulation model.
Fig. 14 is a diagram showing the intensity distribution when there is no periodic structure. Fig.
Fig. 15 is a diagram showing the intensity distribution when there is a periodic structure. Fig.
Fig. 16 is a graph in which the luminance of each analyzed pattern is calculated, and the luminance increase / decrease ratio in the case where the photonic crystal pattern for the no-pattern at the degree m = 3 is plotted as a function of R / a.
Fig. 17 is a graph showing the luminance increase / decrease ratio in the case of having the photonic crystal pattern for the non-pattern at a degree m = 3 as a function of the aspect ratio by calculating the luminance of each analyzed pattern.
Fig. 18 is a diagram showing an example of a manufacturing process of the semiconductor light emitting device (LED) shown in Fig.
19 is a diagram showing an example of a manufacturing process of the semiconductor light emitting device (LED) shown in Fig.
20 is a view showing an example of a manufacturing process of the semiconductor light emitting device (LED) shown in Fig.
Fig. 21 is a diagram showing an example of a manufacturing process of the semiconductor light emitting device (LED) shown in Fig.
22 is a diagram showing an example of a manufacturing process of the semiconductor light emitting device (LED) shown in Fig.
23 is a view showing a graph of an incident angle and a reflectance in the case where a vacancy is photonically crystallized in sapphire.
24 is a view showing a state in which a polyimide tape P is attached to a checkerboard pattern in a wafer and dry etching is performed.
25 is a view showing a top view and a cross-sectional photograph of a sapphire substrate in an epitaxial preparation state, in which the substrate after the dry etching is cleaned to an epitaxial growth ready state.
26 is a diagram showing the measurement results of the LED of Example 1. Fig.
27 is a diagram showing the measurement result of the LED of the second embodiment.
28 is a spectral diagram showing the wavelength distribution of light emitted from the active layer of the LED.
29A is a flowchart showing an example of processing when the depth h of step S7 is a variable of period a (0 <h <5.0a).
29B is a flowchart showing a second step of determining a period (a) and a diameter (d) of the periodic structure by a first step of obtaining a dielectric band and a difference between the dielectric band and the air band.
29C is a flowchart showing the first step divided into four more detailed steps.
30 is a diagram showing an example of a simulation model (extra-intracreate LED) using the FDTD method.
Fig. 31 is a diagram showing output wavelength characteristics (side walls), showing the relationship between the sum of the outputs detected by the monitor disposed on four outer surfaces and the wavelength dispersion. Fig.
Fig. 32 is a diagram showing the output wavelength characteristics (bottom front face), showing the relationship between output values and wavelength dispersion detected in a monitor disposed on the bottom front. Fig.
Fig. 33 is a diagram showing the output wavelength characteristics (sidewall + bottom front face), showing the relationship between the total output value and wavelength dispersion detected by four side walls and a bottom front monitor.
Fig. 34 is a diagram showing the relationship between the LEE increase rate average and the depth at an output central wavelength and a plurality of dispersed wavelengths (total of five wavelengths), and shows data on the sidewall, the bottom front, and the sidewall + bottom front.
Fig. 35 is a diagram showing the output ratio depth characteristics, showing the respective data of the side wall / (sidewall + bottom front) and bottom front / (sidewall + bottom front).
Fig. 36 is a diagram showing a model processed on the surface of the substrate while the photonic crystal periodic structure shown in Fig. 30 is provided on the back surface of the sapphire substrate as an FDTD simulation model (in-focus LED).
37 is a diagram showing an example of a FDTD method simulation model (blue LED).
Fig. 38 is a diagram showing the output wavelength characteristics (side walls), showing the relationship between the sum of the outputs detected by the monitor disposed on the four sides of the side wall and the wavelength dispersion. Fig.
Fig. 39 is a diagram showing the output wavelength characteristics (upper front face), showing the relationship between the output value and the wavelength dispersion detected by the monitor disposed on the upper front face. Fig.
Fig. 40 is a diagram showing the output wavelength characteristics (sidewall + upper front surface), showing the relationship between the total output value and wavelength dispersion detected on four side walls and the top face monitor.
Fig. 41 is a view showing the LEE increase rate depth characteristic, in which data of side walls, top front, sidewall + top front are described.
Fig. 42 is a view showing the output ratio depth characteristics, and shows data of side walls / (sidewalls + upper front) and upper front / (sidewalls + upper front).
43 is a view showing a model in which a photonic crystal is processed on two surfaces of a sapphire substrate surface and SiO ₂ with respect to the FDTD simulation model (blue LED) shown in Fig.

Hereinafter, the semiconductor light emitting device according to the embodiment of the present invention will be specifically described by taking an example of an extra-bright LED element as an example. 1A and 1B described above is an example of a structure applicable to the semiconductor light emitting device according to the embodiment of the present invention. Hereinafter, the structure of FIG. 1A will be described as an example. 1A includes a sapphire substrate (substrate) 1, an AlN buffer layer (buffer layer) 3, an n-type AlGaN layer (n-type cladding layer) 5, an AlGaN active layer and a p-type AlGaN layer (p-type cladding layer) 9, and the light from the AlGaN active layer 7 functions as an LED taken out from the back surface of the sapphire substrate 1 and has a central wavelength of 280 nm . Structure of the blue LED in Fig. 1b is a protective film made of a sapphire substrate (21), n-type GaN layer (23), GaN active layer (25), p-type GaN layer 27, the transparent electrode layer 29 consisting of ITO, SiO ₂ (31), and its central wavelength is 455 nm. In the n-type AlGaN layer (n-type cladding layer) 5, an n-type electrode 4 is formed (the same applies hereinafter).

Hereinafter, an example using the AlGaN active layer or the GaN active layer with respect to the structural example of the semiconductor light emitting device according to the present embodiment will be described taking an extra-pixel LED element and a blue LED element as an example. FIG. 2A is a view showing an example of a first structure of an extra-intense LED element, and corresponds to FIG. 1A. 2 (d) is a view showing an example of a first structure of a blue LED element, which corresponds to Fig. 1 (b).

As shown in Fig. 2A, a two-dimensional photonic crystal periodic structure 15 is formed on the back surface (light-extraction surface) 1a of the sapphire substrate 1, for example. The photonic crystal periodic structure 15 includes a hole 15a for opening the light extraction surface 1a to a predetermined depth as shown in FIG. Are periodically formed along the X direction and the Y direction in the substrate back surface 1a forming the XY two-dimensional plane (see Fig. 3). The back surface portion 15b of the substrate may also be formed by cutting away the original substrate by a shallower depth than the space 15a.

2 and 3, two systems (structures) having different refractive indices are formed on the substrate 15a and the back surface of the substrate 15b, the upper surface of the substrate 17a and the upper surface of the substrate, public (20a) and SiO ₂ A protective film is used, but these are merely examples, and a combination of structures made of different materials may be used. As shown in Fig. 2A, for example, the openings 15a may also have a bottom portion, and the periodic structure may not be a complete periodic structure, and the region to be formed is not the entire XY plane It is good.

2B shows a structure in which the second periodic structure 15 is formed at a position on the side of the AlN buffer layer 3 opposite to the periodic structure 15 of the sapphire substrate 1 in addition to the first periodic structure 15 shown in Fig. (17). The second periodic structure 17 may be formed by burying a sapphire hole and filling it with a material equivalent to an AlN buffer layer. Or a sapphire pillars may be formed.

2C shows a structure in which the third periodic structure 15 is formed at an arbitrary position on the side of the AlN buffer layer 3 corresponding to the periodic structure 15 of the sapphire substrate 1 instead of the first periodic structure 15 shown in Fig. (18). The third periodic structure 18 may be formed by embedding a material having a refractive index lower than that of sapphire. Alternatively, after the third periodic structure 18 is formed on the back surface of the sapphire substrate 1, a layer made of sapphire or another material may be attached.

FIG. 2D shows a fourth periodic structure 20 provided with a reflective film 15 on the back side and a SiO ₂ protective film 31 in which a hole 20a is periodically provided.

In addition, in the face-up structure, a photonic crystal periodic structure may be formed on both the surface of the sapphire substrate and the surface of the SiO ₂ protective film 31.

2E shows a case in which a reflective electrode 31 is provided in place of the SiO ₂ protective film 31 and the ITO transparent electrode 29 shown in FIG. 2D and the back surface of the sapphire substrate 1 Plane) 1a in which a photonic crystal periodic structure 15 is formed.

2F shows a structure in which a second periodic structure is formed at a position on the side of the GaN buffer layer 3 opposite to the periodic structure 15 of the sapphire substrate 1 in addition to the first periodic structure 15 shown in Fig. 17). The second periodic structure 17 may be formed by piercing the sapphire 21 and filling it with a material equivalent to the GaN buffer layer 22. Alternatively, a pillar may be formed on the sapphire 21.

Hereinafter, the parameters of the periodic structure will be described in detail on the basis of the simulation results, taking as an example a photonic crystal having a photonic periodic structure on the surface (back surface) of the sapphire substrate (Fig. 2A). Even if other structures are used, the operation is the same.

First, the structure and device characteristics were determined by simulation in the determined device structure. The method used in this simulation is a method using the plane wave expansion method and the FDTD method (finite difference time domain method). In the plane wave expansion method, by analyzing the band structure of the photonic crystal, it becomes possible to theoretically analyze the peculiar physical properties of the photonic crystal. Further, by obtaining the photonic band gap, the pattern shape in which the light transmittance is maximized (Diameter, cycle, and depth) of the workpiece can be easily obtained. However, it is impossible to obtain the three-dimensional information of the intensity and the angular distribution of the outgoing light with respect to the incident light at the photonic crystal boundary surface. Therefore, the combination with the three-dimensional FDTD method enables pattern shape optimization in a short time.

The technique used in the simulation according to the present embodiment uses the plane wave expansion method and the FDTD method (time domain differential method). In the plane-wave expansion method, by analyzing the band structure of the photonic crystal, the theoretical analysis of the specific physical properties possessed by the photonic crystal becomes possible. Further, by obtaining the photonic band gap, the pattern shape (diameter, Can be easily obtained. However, in the plane wave developing method, it is impossible to obtain the three-dimensional information of the intensity of the emitted light and the angular distribution with respect to the incident light at the photonic crystal boundary surface. Therefore, by using the three-dimensional FDTD method in combination, it becomes possible to carry out arithmetic processing of pattern shape optimization in a short time.

Fig. 3 is a view corresponding to Fig. 2 (b), showing a two-dimensional arrangement of the cavity 15a viewed from the rear surface of the substrate and the remaining portion 15b on the back surface of the substrate. As the parameters of the periodic structure, it is first necessary to determine the period (a) between the cavities 15a and the radius R of the cavities 15a in the upper left x-y coordinate.

Next, the simulation method according to the present embodiment will be described. 4 is a flowchart showing an example of processing when the depth h of step S7 is a variable of the diameter d (2R) (0 &lt; h &lt; 1.0d).

First, conditions for Bragg scattering are given in steps S1 to S3. In step S1, R / a (0.15 &lt; R / a &lt; 0.45) is determined from the circular hole R and the period a constituting the photonic crystal. Further, the refractive index (n ₁ , n ₂ ) of the medium constituting the above and the average refractive index (n _av ) from R / a are obtained.

Fig. 6 is a diagram showing an example of a procedure for obtaining an average refractive index (n _av ). The area ratio of the right circle (V) and the diamond (W) becomes 2? / 3 ^0.5 * (R / a) ² . Refractive index (n _1), the refractive index (n ₂₎ of the sapphire, and when the average refractive index to the R / a = 0.4, n1 = 1.0, n2 = 1.82 (n av) of the public (air) is expressed by the following equation.

n _av ² = n ₂ ² + (n ₁ ² -n ₂ ² ) * area ratio

= 1.82 ² + (1 ² -1.82 ² ) * 0.58 = 1.97

Therefore, the average refractive index (n _av ) is obtained as 1.40.

In fact, the left periodic structure can be transformed into a form in which there is one vacancy (V) in the diamond (W) as shown on the right. The reason is that if you add the left-hand debt (A, B, C, D) to each other, one circle is completed.

Next, in step S2, the wavelength (?), Order (m) (integer: 1 <m <5) and average refractive index (n _av ) are input to the scattering condition of Bragg, 3, and 4).

1 &lt; m &lt; 5 in the formula of m? / n _av = 2 a is as follows.

For example, a photonic crystal periodic structure is publicly formed on the back surface of the sapphire substrate 1. A wavelength: 280 nm, a refractive index at 280 nm of sapphire: 1.82, and an air refractive index: 1.0, where R _av = 0.4, n _av : average refractive index is 1.40. Substituting these values and m = 2, 3, and 4 into the Bragg scattering condition in turn results in the following.

I) When m = 2

2 * 280 / 1.40 = 2 * a

Therefore, a = 199.

Ii) When m = 3

3 * 280 / 1.40 = 2 * a

Therefore, a = 299.

Iii) When m = 4

  4 * 280 / 1.40 = 2 * a

  Therefore, a = 399.

Although the value of m can be increased, the value of the photonic crystal cycle (a) also becomes larger. Therefore, the order m is used so that it does not deviate from the wavelength 280 nm of the intracardiac external light. When calculating the m = 2 and 3 which value of the order (m) is the most effective for the light extraction efficiency, the light extraction efficiency of m = 3 was good.

In step S3, the radius (R) of the circular hole is obtained for each degree (m) from the previously determined R / a and the obtained a. Further, the dielectric constant (? ₁ ,? ₂ ) is obtained by squaring the refractive index (n ₁ , n ₂ ). The relationship between the permittivity (ε) and the refractive index (n) is obtained from n ² = με / μ ₀ ε ₀ , which is obtained by multiplying the refractive index (n ₁ , n ₂ ) to obtain ε ₁ and ε ₂ , respectively.

An analysis by the plane wave expansion method is performed in steps S4 to S6.

First, in step S4, a band structure (TE) of each of TE light and TM light is calculated by inputting the already obtained wavelength (?), Dielectric constant (? ₁ ,? ₂ ) and R / a into Maxwell's electromagnetic wave equation Y axis:? A / 2? C and the x axis: ka / 2 ?. The result will be described later with reference to FIG.

In step S5, PBG (photonic band gap) is obtained from each dielectric band (first photonic band) of TE light and TM light and air band (second photonic band) with reference to FIG. In step S6, the process returns to step S1, and steps S2 to S5 are repeated by selecting several points with R / a as a variable, and PBGs per R / a are selected by selecting several points of R / a, I ask.

Next, in steps S7 and S8, an analysis is performed by the FDTD method. First, in step S7, the diameter d and the period a corresponding to the degree m from the R / a obtained in step S6 are determined to determine the depth h (0 <h <1.0d). The circular hole made up of d, a, and h is set as a periodic structure at the interface of two mediums (refractive index is n ₁ , n ₂ ) and analyzed by the FDTD method to obtain the light extraction efficiency and the light distribution. For example, if the degree (m) = 3, R / a = 0.4 where PBG becomes the maximum, and R = 120 and d = 240. When determining the depth h (0 &lt; h &lt; 1.0d), h = 240 because it simply means 1.0 times the diameter d.

In step S8, the periodic structure is set as an initial condition with d, a, and h as variables, and step S7 is repeated to obtain light extraction efficiency and light distribution. Finally, PBG, light extraction efficiency, and light distribution data corresponding to d, a, and h are obtained.

The result will be described later. The intensity (I) in the case of the periodic structure of FIG. 15 is determined in the same manner, and the light extraction efficiency is obtained from the intensity (FIG. 14) .

The luminous intensity distribution is shown as an electric field intensity distribution diagram corresponding to the angles of Far-filed electric field components (Ex, Ey, Ez) at the bottom of Fig. Here, the luminance of each electric field component is represented by the value of Integral [E] ^ 2 under each of the figures, and the numerical value is higher than that in the case where there is no corresponding periodic structure in Fig. In addition, it is possible to identify the bright portion near the center of the far-field electric field distribution diagram, and thus it can be judged that the frontal luminance is higher than the case where there is no corresponding periodical structure.

5 is a diagram showing an example of processing when the depth h of step S7 is a variable of period a (0 <h <1.0a). (D) and the period (a) corresponding to the degree m from the R / a obtained in the step S6 to obtain the depth h (0 &lt; h &lt; 1.0 a) is determined.

Table 1 shows the dispersion relationship (hereinafter, referred to as &quot; band structure &quot;) of the selected parameter and the frequency (?) And the wavenumber (k) of the light obtained in the parameter selected when simulating the dispersion relation between the frequency and the wave number of the light by using the plane wave expansion method ) In the presence or absence of a bandgap due to the photonic crystal effect and its size.

As a pattern of the periodic structure, air holes are arranged in a triangular lattice pattern on a sapphire substrate. The parameters used in the simulation are the refractive index of sapphire (1.82), the refractive index of air (1.0), R: radius (nm), a: period (nm), m: order, PBG: photonic band gap to be.

Fig. 7 shows a band structure at R / a = 0.4 calculated as an example, and Fig. 8 shows a grating band structure in a case where a sapphire surface is flat as a comparison object.

In Fig. 7, TE denotes a transversal electric (TE) mode in which the electric field exists in the transverse direction with respect to the hole, and TM denotes the TM (transversal magnetic) mode in which the magnetic field exists in the transverse direction with respect to the hole. 7, the dispersion relationship between the frequency () and the wave number (k) is discrete in each of the bands of the TE mode and the TM mode, and the dispersion relationship between the frequencies ω1TE (dielectric band) and ω2TE The photonic band gap (PBG) is observed and the difference in shape is clear when compared with the result of the grating band structure in the flat case of FIG. 8 having an intersection point (CP).

This phenomenon, which is obvious when comparing FIGS. 7 and 8, is that in the TE mode, the electric field is parallel to the two-dimensional plane, and when a thin linear dielectric is connected to the network structure, the electric field of the TE mode becomes easy to stay in the connected dielectric . In other words, the photonic band gap (PBG) can be easily opened in the TE mode because the photonic bandgap can be stably energized.

Next, paying attention to the ω2TE band in order to consider the characteristics obtained when the photonic band gap (PBG) is opened, it is found that at the band edge, the propagation speed ) Velocity is determined by the group velocity Vg and Vg = dω / dk, Vg = 0), and it can be seen that the optical transmittance increase due to the photonic crystal effect can be expected.

7 is an analysis of a part of a band edge (a portion surrounded by points, M points, and K points) in the first Brillouin region. Here, the wave number vector kx , ky) is obtained, and R / a = 0.25 is shown in Fig. 9 and R / a = 0.4 is shown in Fig.

The direction of light propagation in the photonic crystals is determined by the group velocity, and the wavevector vector k is required to obtain the group velocity. This can be seen from the iso-frequency side as shown in Figs. 9 and 10. Fig. As shown in Fig. 3, when the light of frequency (ω) is transmitted from the sapphire region 15b in the two-dimensional space (x, y) to the photonic crystal, the momentum in the tangential direction with respect to the incident surface is preserved. If this phenomenon is expressed by the wave space (kx, ky) (where k = 2πa and a is a period), the y direction component (ky) of the wavenumber vector in the photonic crystal is expressed by ky _a / 2π = ωa / 2πc · sinθi .

The group velocity is a gradient from the above-mentioned expression Vg = d? / Dk to the wavenumber vector of the frequency, and the normal direction of the equal frequency plane is directed in the direction of increasing frequency, Direction. In particular, the point at which the group velocity anomaly is observed is the coordinate (kx, ky) = (-0.283, 0.491) of the constant frequency plane ωa / 2πc = 0.55 in FIG. When ky = 0.491 is substituted into the expression ky _a / 2π = ωa / 2πc · sinθi, θi = 63 ° is obtained. On the other hand, the transmission direction of light is the arrow direction, and the magnitude of the refraction angle θr is obtained from the expression tanθr = (ky / kx) to -60 °. Therefore, it can be seen that the relationship between the angle of incidence and the refracting angle is θi> 0 and θr <0, indicating a state of a real refractive index n <0 and a negative refraction effect.

Fig. 12 shows a case where R / a = 0.25, and Fig. 12 shows a case where R / a = 0.4 in relation to the angle of incidence with respect to the incident angle. In Figs. 11 and 12, θi and θr are always opposite to each other and exhibit a negative refraction effect. Further, in the band end Γ point vicinity, and the change of the large angle of refraction measured by a slight angle of incidence changes, the other band end the K point, but a large difference in the change of the incident angle and the refractive angle to the angle of incidence is larger than the critical angle θ _c = 33.3 ° Suggesting an increase in transmittance due to the photonic crystal effect. The relationship between R / a and the transmittance (i.e., light extraction efficiency) and the relationship between the size of the PBG (photonic band gap) and the light transmittance And that there is a correlation with the extraction efficiency.

Next, simulation results are shown by the FDTD method using the pattern shape obtained by the above-described plane wave expansion method. 13 is a diagram showing an example of a FDTD method simulation model. Light emission hν is generated from the light source in the sapphire substrate 1 through the photonic crystal periodic structure 15 formed on the light extraction surface which is the back surface 1a of the substrate 1 as shown in FIG. Here, a monitor of light is disposed at a position a predetermined distance from the back surface 1a of the substrate 1. [

A space of 10 mu m x 10 mu m x 6.5 mu m was set as an analysis area, and a photonic crystal, a monitor, and a light source were arranged at a suitable place inside. The grid size for dividing the space is 20 nm, and a full absorption boundary condition is set for preventing reflected waves at the space boundary, and a dipole single light source, which is in principle close to the LED light source, is used as the light source.

14 is a calculation result when there is no pattern of the periodic structure on the back surface of sapphire. The near-field electric field component from (a) to (c) , Ey, and Ez components. Far-field electric field components from (d) to (f) are obtained by Fourier transforming x, y of the Near-field electric field component and calculating the electrolytic distribution of the wavenumber space field angular distribution) are shown for each Ex, Ey, and Ez component.

In the FDTD simulation, as shown in Table 2, by changing the order (m = 3), R / a (0.25, 0.3, 0.35, 0.4) and the aspect ratio (0.5, 1.0 and 1.5 in depth / The brightness of the photonic crystal pattern was analyzed. Fig. 15 is a diagram showing an analysis result of a pattern of order (m) = 3, aspect ratio 0.5, R / a = 0.4, diameter / period = (239 nm / 299 nm) as an example. (a) to (c) show the near-field electric field components, and (d) to (f) show the far-field electric field components. Generally, the light intensity I is represented by the following equation using the field component (Ex, Ey, Ez) of the circular arc system (? ₀ : dielectric constant in vacuum, c: light speed).

_{I = ε 0 * c (Ex} 2 + Ey 2 + Ez 2)

Using this equation, the luminance of each pattern analyzed this time is calculated, and the luminance increase / decrease ratio in the case of having the photonic crystal pattern for the no pattern at the degree (m) = 3 is expressed as a function of R / a and the aspect ratio 16 and 17, respectively.

In Fig. 16, when the aspect ratio is 0.5, there is clearly a tendency of a difference in comparison with the graphs of the other aspect ratios 1.0 and 1.5. The pattern used here is obtained from the formula: mλ / n _av = 2a, m: order, a: period, and λ: wavelength satisfying the scattering condition of Bragg.

In the above-described plane wave expansion method, if the photonic bandgap is large, the magnitude of the R / a and the photonic band gap is large, and the light is refracted even at an incident angle that causes total internal reflection. Normally, in the case of a two-dimensional triangular lattice photonic crystal, a photonic band gap is opened as a symmetric point, and two and three standing waves are respectively generated at the symmetric points M and K at that time. A standing wave is an interference of two or more waves of the same frequency traveling in different directions, and the amplitude is determined by the traveling direction of two or more waves. Therefore, in this case, the effect of increasing the luminance was obtained by the influence of the standing wave, as compared with the case of R / a: 0.35. It can also be seen that this tendency is also seen in a wide aspect ratio as shown in Fig.

As described above, the photonic crystal pattern and the laws concerning the luminance are summarized as follows.

1) In the depth direction, the luminance increase rate is the maximum at an aspect ratio of 0.5.

2) In the relationship of R / a, R / a: 0.3 or R / a: 0.4 is ideal. The fact that the effect of photonic crystal is easily obtained when R / a is close to 0.4 means that the average refractive index at this time is an intermediate value between sapphire and air, which is a reasonable result even if it contributes to a large change in the dielectric constant.

Table 3 shows the photonic bandgap magnitudes at the interface between the sapphire substrate surface and the GaN layer. Table 4 shows the magnitude of the photonic bandgap at the interface between the sapphire substrate surface and the GaN layer. In the protective film and the air layer, when the R / a is 0.35, the photonic band gap is the largest and the light extraction efficiency is improved. Similarly, when R / a is 0.3 at the interface between the sapphire substrate surface and the GaN layer, the photonic band gap is the largest and the light extraction efficiency is improved.

29A to 29C, a more optimal condition has been considered with respect to the processing depth h of the photonic crystal periodic structure.

29A is a flowchart showing an example of processing when the depth h of step S7 is a variable of period a (0 <h <5.0a). FIG. 29B is a flowchart showing a second step of determining a period (a) and a diameter (d) of the periodic structure by a first step of obtaining a dielectric band and a difference between the dielectric band and the air band. FIG. 29C is a flowchart showing the first step by dividing it into four more detailed steps.

29A, the simulation range of the depth h using the FDTD method in step S7 is extended to 0 &lt; h &lt; 5.0a in the flow of the simulation described with reference to Figs. 4 and 5 (Step S7a).

29B, first, in step S11, as a process of selecting two structures having different refractive indices, a ratio (R / a) between a period (a) and a radius (R) satisfying a scattering condition of Bragg at a design wavelength ) As parameters, a photonic crystal periodic structure composed of two structures having different refractive indices is selected. Next, as a first step of obtaining a dielectric band (first photonic band) in step S12, Maxwell's electromagnetic field wave equation of a plane wave output from the photonic crystal periodic structure developed by an electric field (E) and a magnetic field (H) ^{Σε -1 (GG ') | k} + G || k + G' | E (G ') = ω 2 / c 2 E (G') and ^{_{Σ ε -1 (GG ') (}} k + G) * (k + G') H (G ^{') = ω 2 / c 2} H (G), (ε -1: inverse of the dielectric constant, G: reciprocal lattice vectors, ω: frequency, c: light beam, k: TE light from the eigenvalue calculation of the wave number vector) or TM light (First photonic band) is obtained.

Next, as a second step of determining the period (a) and the diameter (d) in step S13, a period a in which the difference between the dielectric band (first photonic band) and the air band (second photonic band) ) And the diameter (d).

29C, in step S21, the ratio R / a of the radius R and the period a constituting the photonic crystal periodic structure is selected within the range of 0.15 to 0.45 as the process of giving the condition (parameter) of Bragg scattering Then, the design wavelength λ to obtain the effect of the photonic crystal is determined, and the average refractive index (n _av ) is determined from the refractive indices n1 and n2 of the selected two structures.

Next, in step S22, the period (a) is calculated for each degree (m) (m = 1, 2, 3, ...) from m? / N _av = 2a from the Bragg scattering condition, . In step S23, as the diameter R of the periodic structure and the dielectric constant, the radius R for each degree m is calculated from the already selected R / a, and from the refractive indexes of the two structures selected equally, To calculate respective dielectric constants (? ₁ ,? ₂ ). In Step S24, the design wavelength λ, the dielectric constant (ε ₁ , ε ₂ ), and R / a are input to the Maxwell electromagnetic wave equation as eigenvalue calculation processing in Maxwell's electromagnetic wave equation.

30 is a diagram showing an example of a FDTD method simulation model in the extra-bright LED structure. In addition, the method of specifically calculating the diameter d, period (a), and depth (h) of the periodic structure is the same as the above-described method and therefore will not be described here. When a value of R / a is obtained, a is uniquely determined by the relational expression d = 2 R, so that the depth h may be a variable of the diameter d as described above.

In consideration of the optimization for the depth h, in the case of a monitor for detecting the intensity of light, light emitted from the well layer proceeds in all directions. Therefore, considering the structure of the semiconductor light emitting device, And four sidewalls were arranged in total. The intensity of light detected by the monitor is the absolute value of the external (external) product of the electric field and the magnetic field, and the unit is [W]. The reason for placing the monitor outside the LED structure is that when the light inside the LED is emitted to the outside, there is a difference in refractive index between the LED and the air, and the LED is totally internally reflected according to Snell's law.

In addition, the light emitted from the well layer was absorbed by the p-type GaN contact layer, and therefore, the simulation was performed after changing to the p-type AlGaN contact layer without absorption. Therefore, the structure can achieve LEE equivalent to blue LED.

As the analysis area, a space of 8 mu m x 8 mu m x 6 mu m is set and a grid size of 10 nm for dividing the space is set to a perfect absorption boundary condition for the purpose of preventing the influence of reflected waves on the outside of the monitor, A dipole light source, which is in principle close to the LED light source, was used.

The analysis results shown in Figs. 31 to 33 show the light distribution characteristics as output values respectively detected at the side wall and the bottom front surface, and the light detected at the bottom shows the luminance of the front surface. 34 shows the relationship between the LEE increase rate at the sidewall, the bottom front, and the sidewall + bottom front and the depth h indicated by the variable of the period a of the periodic structure. Since the face-down (flip-chip) type is the mainstream in the actual non-optical LED element, in this case, the upper face portion is fixed to the seat. Therefore, the surface from which the light is extracted becomes the side wall portion and the bottom front surface, and in particular, the LEE increase rate characteristic of the front surface as the front becomes important.

As can be seen from FIG. 34, as the depth h of the periodic structure becomes deeper, the increase rate of the side wall portion LEE increases. This is because, when the depth (h) is deepened, the surface area of the region capable of obtaining the Bragg scattering effect is increased, and the increase in the LEE increase rate is almost proportional to the depth (h). The same phenomenon is recognized at each wavelength.

On the other hand, the bottom frontal LEE increase rate increases sharply in the range of the depth h of the periodic structure up to 0.5 times of the period (a), and the value is close to 50%. Thereafter, the LEE growth rate is gradually increased or decreased, so that the depth h is substantially lagged after 2.0 times the period a. That is, the effect of increasing the LEE increase rate due to the phenomenon unique to the photonic crystal periodic structure having the photonic band gap is most effective when the depth h of the periodic structure is 0.5 to 2.0 times the period (a).

From the above, the sum of the LEE increase rate of the entire LED element, that is, the increase rate of the sidewall LEE and the increase rate of the bottom front LEE is remarkable when the depth h of the periodic structure is 0.5 times or more of the period (a).

In Fig. 35, the output ratios of the sidewall / (sidewall + bottom front) and bottom front / (sidewall + bottom front) in the range of 0 <h <5.0a are compared. Here, the case where the depth (h) = 0 indicates the case where there is no periodic structure. According to this, in the range of the depth h of 0.5a <h <5.0a, the respective output ratios are changed to approximately 6: 4. This ratio is related to the area ratio of the side wall and the bottom face, and can be changed, for example, by changing the thickness of the sapphire substrate.

In order to increase the output ratio of the bottom surface / (sidewall + bottom surface) more specifically, it is necessary to increase the area when the substrate is split in the plane and to reduce the thickness of the sapphire substrate (several hundred mu m). In this case, it is preferable to adjust the thickness of the sapphire substrate to be smaller than the thickness (several 占 퐉) of the semiconductor portion. The light distribution of the LED element can be adjusted by adjusting the area ratio.

36 shows a model result obtained when a photonic crystal periodic structure is added to the surface of the substrate in addition to the back surface of the sapphire substrate of the extra-bright LED structure to perform a simulation. Each photonic crystal pattern had a hole shape with a diameter of 230 nm, a period of 287 nm and a depth h of 1.0 times as large as the period a. The substrate surface had a pillar shape with a diameter of 299 nm, a period of 415 nm, The depth (h) is 1.0 times the period.

As shown in the graph of 1.0a + Pillar in Figs. 31 to 33, the output value of the sidewall, the bottom front, the sidewall, and the bottom almost all exceeded the output value of the photonic crystal of the hole 1.0a monomer. The LEE growth rate is shown in the following table.

Side wall Bottom front Side wall + bottom front Hole 1.0a 10% 53% 25% Hole 1.0a +
Pillar 1.0a 35% 49% 40%

As a result of Table 5, when the photonic crystal periodic structure was processed on both sides of the sapphire substrate, the LEE increase rate of the entire LED device was further increased by 15 points, that is, 40% as compared with the back side process.

Similarly, FDTD simulation was performed on the blue LED structure. 37 shows the structure thereof. The analysis results shown in Figs. 38 to 40 were analyzed by the plane wave expansion method and the FDTD method through steps S1 to S8 in Fig. 29 as described above. (A) = 415 nm, a diameter (d) = 299 nm, and a degree (m) = 4, and the output value detected at the side wall and the upper front surface exhibits the light distribution characteristic, And the light detected at the front surface represents the luminance of the front surface.

In a practical blue LED element, a face-up structure is the mainstream. In this case, since the bottom portion is fixed to the pedestal, the side from which light is extracted becomes the side wall portion and the upper front surface. And Fig. 41 shows the relationship between the increase rate of the LEE and the depth (h) at the sidewall, the upper front surface, and the sidewall + upper front surface.

As can be seen from Fig. 41, the LEE increase rate of the side wall increases at least approximately in proportion to the depth h in the range of the depth h from 0.5a to 5.0a. Therefore, the increase rate of the LEE on the sidewall + top face, that is, the LEE increase rate of the entire LED device, is not nearly dependent on the correlation between the depth (h) and the LEE increase rate on the top face, Increase. Also, the output ratio depth characteristics of the side wall and the upper front surface are approximately 35:65 as shown in Fig.

Also Fig. 43, the blue LED structure SiO ₂ And a photonic crystal is added to the protective film to perform simulation. Pattern of each photonic crystal, the substrate surface is in pillar diameter: 299nm, period: 415nm, a depth (h) is 1.0 times of the period (a), and, SiO ₂ The protective film is a hole having a diameter of 499 nm, a period of 713 nm, and a depth h of 260 nm because the film thickness of the SiO ₂ protective film is limited to 300 nm. LEE growth rate is shown in the following table.

Side wall Top face Side wall + upper front Pillar 1.0a 18% 37% 24% Pillar 1.0a + hole 260nm 17% 45% 27%

As a result of Table 6, when the photonic crystal was processed on the surface of the sapphire substrate and the back surface of the SiO ₂ protective film, the LEE increase rate of the entire LED device was increased to 3 points, that is, 27% as compared with the surface only processing.

Next, the manufacturing process of the photonic crystal mounted LED will be described.

<Examples>

[Example 1]

Figs. 18 to 22 are diagrams showing examples of a part of the manufacturing process of the semiconductor light emitting device (LED) shown in Fig. 1 (a procedure for preparing a photonic crystal structure).

First, as shown in Fig. 18, a quartz mold (master mold) 100 for preparing a periodic structure is prepared. The mold pattern 103 of the substrate 101 has R / a = 0.3, a diameter, a period, and a depth of 155 nm, 263 nm, and 361 nm, respectively.

For photonic crystal processing of a sapphire substrate, resist patterning is performed by a nanoimprint, and subsequently, sapphire is dry-etched using a resist by ICP etching as a mask. However, a stepper such as a KrF is used for fine patterning of a 100 nm order, and there is a problem that a side effect is caused in exposure when the cost is increased and the substrate is warped.

On the other hand, in the case of the nanoimprint process, if the sapphire substrate or the nitride semiconductor layer is warped or the like, the mold pattern may be broken if pressure / UV transfer is performed directly on the resist on the sapphire substrate with the quartz mold. (B) a film mold 110 (111, 113) is formed from a quartz mold 100 as shown in the figure and then the film mold 110 is coated with a resist A method of transferring the pattern 125 onto the substrate 123 is adopted. (d) to (g) are SEM photographs showing the shapes of actual patterns.

According to this method, it is possible to sufficiently transfer the substrate to warp and minute projections. Etching of sapphire after pattern transfer is performed as ICP etching as shown in Figs. 19 and 20, and processing with high precision is extremely difficult. The single crystal sapphire does not dissolve in either acid or alkali, and the etching selectivity ratio to the sapphire of the resist is insufficient. In general photoresist for photoresist, the selection ratio is generally about 0.5 to 0.7. In the UV curable nanoimprint, the flowability of the resist and the selectivity after curing are in a trade-off relationship, and the selectivity is 0.5 or less, which is not a sufficient value.

In the first embodiment, optimization of the mold pattern, optimization of resist patterning by nanoimprint, and optimization of sapphire processing by ICP dry etching are performed to form a triangular lattice array of air holes on the back surface of the sapphire substrate as shown in Fig. The spectral ratios 0.5 and 1.0 and the same photonic crystal pattern as the design can be obtained to establish the process technology (diameter 127 nm / cycle 252 nm / height 359 nm).

When the sectional view of the photonic crystal after the dry etching is actually observed, as shown in the figure, the taper angle is about 75 to 80 degrees rather than the complete spherical shape. In the simulation, there is a slight numerical change because it is done with a perfect rectangle.

23 is a view showing a graph of an incident angle and reflectance when a sapphire is subjected to photonic crystal processing to form a vacancy. It can be seen that in the case of a completely rectangular shape, reflection of about 3 to 5% is generated. The reason is that a sudden change in the refractive index occurs at the interface between air and sapphire (in this case, R / a is 0.4, and the average refractive index is 1.4). On the other hand, when the taper angle exists in the period in which the concavities and convexities are close to the wavelength, the light is detected such that the refractive index changes gently from the sapphire to the air. Therefore, since there is no interface where the refractive index rapidly changes, the light is not reflected, and the brightness is increased accordingly.

However, in the dry etching process, as shown in Fig. 24, the polyimide tape P was attached to the wafer in the form of a checkerboard, and dry etching was performed. The region where the polyimide tape P is adhered is not dry-etched, and if the organic cleaning is performed, the resist pattern is also lost. This is to make it possible to observe the luminance difference in the presence or absence of the photonic crystal pattern in the same wafer when the crystal grows later to form and evaluate the LED.

Next, the substrate after the dry etching is cleaned to prepare for the preparation of the epitaxial control. Thereafter, crystal growth is carried out by using, for example, a recipe in which predetermined growth conditions are summarized by MOCVD. An electrode is formed on the substrate after the crystal growth, the element is divided, and the wavelength and brightness of the LED are measured by an integrating sphere.

The wavelength of the light emitted from the active layer of the LED is 270 nm, and the spectrum thereof is shown in Fig. 26 is a diagram showing the measurement results of the first embodiment. In FIG. 26, the presence or absence of a photonic crystal pattern is represented by I-V, I-L, and EQE characteristics (I: current, V: voltage, L: output, EQE: external quantum efficiency).

As shown in Table 7, since the average R / a after the dry etching (DE) after the dry etching becomes smaller than the R / a of the mold, the brightness evaluation uses the average R / a after DE.

In Table 1, when the average R / a after DE is 0.257, the effect of luminance can be expected because the photonic band gap is sufficiently wide. However, the measurement result in the case of the depth 80 nm shows that the correlation is observed regardless of the presence or absence of the photonic crystal pattern It was not. It is considered that factors in the depth direction are applied. On the other hand, when the depth is 160 nm, the average R / a after DE is 0.209, so whether or not the photonic band gap shown in Table 1 is opened is subtle. However, there is some correlation with the presence or absence of the photonic crystal pattern. Output increased by 10%. The depth direction may also act a little, and it is judged by comparison with Example 2 below.

[Example 2]

Similarly, a quartz mold 100 is prepared as shown in Fig. The mold pattern 103 has a R / a of 0.38, a diameter, a period, and a depth of 230 nm, 299 nm, and 371 nm, respectively. As in the case of Embodiment 1, the sapphire substrate is patterned by nanoimprinting in the photonic crystal processing, and subsequently the sapphire is dry-etched using the resist by ICP dry etching as a mask. As shown in Figs. 21 and 22 As a result, it was possible to obtain a desired pattern of photonic crystals according to the design with the aspect ratios of 0.5 and 0.8 with a triangular lattice arrangement of air holes on the sapphire substrate backside, thereby establishing the process technology.

Next, the substrate after dry etching is cleaned to be in an etching ready state. FIG. 25 shows a photograph of the shape of the top surface and the cross section of the sapphire substrate in the etching ready state. (a) is a top view, (b) is a cross section, and (c) is an enlarged view of (b). Thereafter, crystal growth is performed using a predetermined recipe by the MOCVD method. An electrode was formed on the substrate after the crystal growth, and the device was divided to measure the brightness of the LED in the integrating sphere.

The measurement results of the LED of Example 2 are shown in Fig.

First, the average R / a value after DE in Table 8 is still 0.263 at 125 nm and 200 nm in the depth direction. If this value is satisfied, the photonic band gap is sufficiently opened also from Table 1, so that the correlation between the presence or absence of the photonic crystal pattern and the luminance can be expected. Actually, the measurement result of FIG. 27 shows the effect of improving the luminance by providing the photonic crystal periodic structure even when the holes have depths of 125 nm and 200 nm. The current output increased by 20 percent. As for the difference in the depth direction, it can be seen that both the applied voltage and the current are larger than those of the depth of 125 nm and the output value itself is also large when the depth is 200 nm.

The upper and lower diameters of FIG. 25 are 249 nm and 162 nm, respectively, which are larger by 59 nm and 37 nm, respectively, than the upper diameter and lower diameter of Table 6. The dry etching of the sapphire substrate is performed by reactive ion etching using a chlorine-based gas, and aluminum is attached to the etching side wall due to the etching while reducing oxygen by cutting aluminum and oxygen, which are components of sapphire, The diameter of the lower part was measured with margin. Assuming that the amount of the side wall deposit is proportional to the etching time, the results of Tables 7 and 8 are corrected and shown in Table 9.

As a result of the correction of Table 9 and the results of Example 1 and Example 2, there is almost a proportional correlation between the photonic bandgap size and the light extraction efficiency, and when the depth direction is equivalent to the diameter, And it was effective.

As a result obtained so far, it has been found that when the dry etching is performed on the sapphire substrate, there is an etching bias value with respect to the shape of the mold and the shape after removal of the resist residue after dry etching. Table 10 shows the results of simulation when a master mold is prepared by correcting the etching bias value so as to obtain an effect as designed, assuming a case of a cycle of 299 nm and a mold R / a of 0.385.

The mold design value for securing the intermediate diameter of 230 nm and the R / a of 0.385 after the dry etching after removal of the resist residue is as large as 30 nm at the intermediate straight view from Table 10 and the angle of the sidewall of the mold is 89.0 degrees Could know. This makes it possible to integrate and manage the processes from photonic crystal design, mold preparation, resist selection, transfer by nanoimprint, and dry etching (process integration).

According to this embodiment, a concave-convex portion made of a two-dimensional photonic crystal having a period equal to the wavelength of light in the medium of the light is processed on the sapphire substrate, the interface between the sapphire substrate surface and the GaN layer, There is an energy region (photonic band gap) in which transmission of light is impossible. Light having a wavelength within the photonic bandgap is not transmitted through the plane in which the periodic structure is formed but is transmitted only in a direction perpendicular to this plane. Therefore, the light emitted from the active layer and emitted from the sapphire substrate or the interface between the sapphire substrate surface and the GaN layer or the protective film is not totally reflected at the interface with the air and is released into the air, resulting in improvement in the light extraction efficiency, And the luminance increases. In addition, the light emitting device has a high frontal luminance.

In the above-described embodiments, the configurations and the like shown in the accompanying drawings are not limited to these, and can be appropriately changed within a range that exerts the effects of the present invention. In addition, the present invention can be appropriately modified without departing from the scope of the present invention.

For example, the design program, the mold designed by the program, and the like are also included in the present invention. The periodic structure composed of another system (structure) may be composed of three or more systems (structures) other than two. The system may be composed of two kinds of crystals as well as air and crystals.

The configurations and the like shown in the accompanying drawings in the above-described embodiments are not limited to these, and can be appropriately changed within a range that exerts the effects of the present invention. In addition, the present invention can be appropriately modified without departing from the scope of the present invention.

In addition, each constituent element of the present invention can be arbitrarily selected and included in the present invention having a selected configuration.

For example, various color light emitting diodes can be produced by using the following materials as materials of LEDs.

· Aluminum gallium arsenide (AlGaAs) - Infrared ray · Red

· Gallium arsenide (GaAsP) - red, light orange, yellow

· Indium gallium nitride (InGaN) / Gallium nitride (GaN) / Aluminum gallium nitride (AlGaN)

· Gallium Phosphide (GaP) - Red, Yellow, Green

· Zinc selenide (ZnSe) - green · blue

· Aluminum indium gallium phosphorus (AlGaInP) - etc. · Yellow · Yellow · Yellow · Green

· Diamond (C) - Ultraviolet

· Zinc oxide (ZnO) - blue, green and near ultraviolet

The following are used as a substrate.

As a substrate, silicon carbide (SiC) - blue

· Sapphire (Al ₂ O ₃ ) as substrate - blue, ultraviolet

As the substrate, silicon (Si)

&Lt; Industrial applicability >

The present invention can be applied to a semiconductor light emitting device. The extra-bright LED is useful as sterilization and purification, and the process technology is useful for mass production.

All publications, patents, and patent applications cited herein are hereby incorporated by reference in their entirety.

One… Sapphire substrate, 1a ... The back surface (light extracting surface) of the sapphire substrate 1, AlN buffer layer, 5 ... n-type AlGaN layer, 7 ... n-type AlGaN active layer, 9 ... p-type AlGaN layer, 15 ... Photonic crystal periodic structure, 15a ... Ball study, 15b ... The back surface of the substrate, 21 ... Sapphire substrate, 23 ... n-type GaN layer, 25 ... n-type GaN active layer, 27 ... p-type GaN layer, 29 ... Transparent electrode layer 31, Shield.

Claims (17)

As a photonic crystal periodic structure composed of two systems (structures) having different refractive indices,
The design wavelength?, Period (a) and radius (R) for determining the photonic crystal periodic structure at the interfaces of the two systems (structures) satisfy the Bragg condition,
The ratio (R / a) between the period (a) and the radius (R) of the period is a value having a maximum photonic band gap of the photonic crystal periodic structure,
The order m of the Bragg condition is an order in which the light extraction efficiency is maximized with respect to the design wavelength lambda by the simulation analysis result using the FDTD method,
And the photonic crystal periodic structure is contained in the light extraction layer. The method according to claim 1,
Wherein a depth h of the photonic crystal periodic structure is 0.5 times or more of a period a of the photonic crystal periodic structure. The method according to claim 1 or 2,
Wherein the light extraction layer is formed on a surface of the semiconductor light emitting device opposite to the substrate or the substrate. The method of claim 3,
Wherein the photonic crystal periodic structure is provided in a region at an arbitrary depth position of the substrate. The method of claim 3,
Wherein the photonic crystal periodic structure is formed to include a cavity formed periodically on the back surface of the substrate. The method according to claim 1,
Wherein the photonic crystal periodic structure is formed in two or more regions within a region at an arbitrary depth position of one or two or more light-extraction layers. The method according to any one of claims 1, 2 or 6,
Wherein the photonic crystal periodic structure having the photonic band gap comprises:
(GG ') | k + G | k + G' | E (G ') = ω ² ( ¹ ) where Maxwell's electromagnetic field wave equation Σε ^-1 (GG') developed by developing the electric field E and the magnetic field H from the plane wave output from the photonic crystal periodic structure / c ² E (G ') and ^{Σε -1 (GG') (k} + G) * (k + G ') H (G') = ω 2 / c 2 H (G), (ε-1: the inverse of the dielectric constant, G (The first photonic band) and the air band (the second photonic band), which are obtained from the eigenvalue calculation of the reciprocal lattice vector, ω: frequency, c: luminous flux, k: ) And the diameter (d), which are parameters of the structure, are determined by the difference between the period (a) and the diameter (d) of the photonic crystal periodic structure. The method of claim 7,
And a photonic crystal periodic structure in which the depth (h) is further determined by the FDTD method. The method according to any one of claims 1, 2 or 6,
Wherein the photonic crystal periodic structure of the light extracting layer is processed using a nanoimprint lithography method. The method of claim 9,
Wherein the photonic crystal periodic structure of the light-extraction layer is processed using a transfer process of a mold pattern through a resin mold. The method according to any one of claims 1, 2 or 6,
Wherein the substrate of the semiconductor light emitting element is sapphire. The method according to any one of claims 1, 2 or 6,
Wherein the semiconductor layer of the semiconductor light emitting element is made of a nitride semiconductor. The method of claim 9,
Wherein the following steps (1) to (3) are used in the nanoimprint lithography method.
1) When a master mold for a nanoimprint is prepared, a resin mold is prepared to cope with the warping of the substrate, and transferred to the resist on the substrate by using the resin mold so that the pattern on the substrate and the master mold pattern are not reversed do.
2) The substrate is etched by dry etching after nanoimprinting. At this time, a mold is formed at a period (a), a diameter (d) and a depth (h), a resin mold is taken therefrom, a pattern is transferred to a resist on the substrate by a nanoimprint, And the actual shape is measured.
3) Reflecting the etching bias value which is the difference between the measured value of the actual shape and the design value, the master mold is again formed, and the transfer, the dry etching, and the resist residue are removed. A method for calculating a parameter of a photonic crystal periodic structure composed of two systems (structures) having different refractive indices,
(R / a) between the radius (R) and the period (a) of the photonic crystal periodic structure at a design wavelength (λ) (S1) of obtaining an average refractive index (n) of the structure (structure)
Step S2 of inputting the average refractive index n of the design wavelength λK to the Bragg condition equation and obtaining the period a and the radius R for each degree m of the conditional equation,
A step S3 of obtaining respective dielectric constants? And? Of the two systems,
The dielectric constant (ε, ε) and the ratio (R / a) obtained in the step S1 to the step S3 are obtained by dividing the plane wave of the design wavelength λ outputted from the photonic crystal periodic structure by the electric field E, the magnetic field H ) electromagnetic wave equation of Maxwell deployed to ^{Σε -1 (GG ') | k} + G || k + G' | E (G ') = ω 2 / c 2 E (G') and ^{Σε -1 (GG ') (k} + G) in (wave number vector ε ^-1: inverse of the dielectric constant, G: reciprocal lattice vectors, ω: frequency, c:: light beam, k) * (k + G ') H (G') = ω 2 / c 2 H (G), (Step S4) of obtaining a dielectric band (first photonic band) of TE light or TM light from its eigenvalue calculation,
(S5) of obtaining a photonic band gap by a difference between the dielectric band and the air band (second photonic band)
A step S6 of repeating the above step S5 from the above step S1 to obtain a ratio (R / a) representing the maximum photonic band gap,
A period (a), a radius R (diameter d = 2R) and a depth h of the predetermined photonic crystal periodic structure determined for each degree m from the ratio R / a obtained in the step S6 A step S7 of obtaining a light extraction efficiency with respect to the design wavelength? By a simulation analysis by the FDTD method,
(A), radius (R), 1 &lt; m &lt; 5, which is a parameter of the photonic crystal periodic structure in which light extraction efficiency is maximized with respect to the design wavelength A step S8 for obtaining the degree m and the depth h,
And calculating a structural parameter of the semiconductor light emitting device. 15. The method of claim 14,
Wherein the parameter (h) is parameterized in a range of 0.5 times or more of the period (a) in the step S8.
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